Marco M. Caldarelli

Thermodynamics of Kerr-Newman-AdS black holes and conformal field theories

We study the thermodynamics of four-dimensional Kerr-Newman-AdS black holes both in the canonical and the grand-canonical ensemble. The stability conditions are investigated, and the complete phase diagrams are obtained, which include the Hawking-Page phase transition in the grand-canonical ensemble. In the canonical case, one has a first-order transition between small and large black holes, which disappears for a sufficiently large electric charge or angular momentum. This disappearance corresponds to a critical point in the phase diagram. Via the AdS/CFT conjecture, the obtained phase structure is also relevant for the corresponding conformal field theory living in a rotating Einstein universe, in the presence of a global background U (1) current. An interesting limit arises when the black holes preserve some supersymmetry. These BPS black holes correspond to highly degenerate zero-temperature states in the dual CFT, which lives in an Einstein universe rotating with the speed of light.

All supersymmetric solutions of N = 2, D = 4 gauged supergravity

We classify all supersymmetric solutions of minimal gauged supergravity in four dimensions. There are two classes of solutions that are distinguished by the norm of the Killing vector constructed from the Killing spinor. If the Killing vector is timelike, the solutions are determined by the geometry of a two-dimensional base-manifold. When it is lightlike, the most general BPS solution is given by an electrovac AdS travelling wave. This supersymmetric configuration was previously unknown. Generically the solutions preserve one quarter of the supersymmetry. Also in the timelike case we show that there exist new BPS solutions, which are of Petrov type I, and are thus more general than the previously known type D configurations. These geometries can be uplifted to obtain new solutions of eleven-dimensional supergravity.

Higher-dimensional rotating charged black holes

Using the blackfold approach, we study new classes of higher-dimensional rotating black holes with electric charges and string dipoles, in theories of gravity coupled to a 2-form or 3-form field strength and to a dilaton with arbitrary coupling. The method allows to describe not only black holes with large angular momenta, but also other regimes that include charged black holes near extremality with slow rotation. We construct explicit examples of electric rotating black holes of dilatonic and non-dilatonic Einstein-Maxwell theory, with horizons of spherical and non-spherical topology. We also find new families of solutions with string dipoles, including a new class of prolate black rings. Whenever there are exact solutions that we can compare to, their properties in the appropriate regime are reproduced precisely by our solutions. The analysis of blackfolds with string charges requires the formulation of the dynamics of anisotropic fluids with conserved string-number currents, which is new, and is carried out in detail for perfect fluids. Finally, our results indicate new instabilities of near-extremal, slowly rotating charged black holes, and motivate conjectures about topological constraints on dipole hair.

More on BPS solutions of N = 2, D = 4 gauged supergravity

We deepen and refine the classification of supersymmetric solutions to N = 2, D = 4 gauged supergravity obtained in a previous paper. In the case where the Killing vector constructed from the Killing spinor is timelike, it is shown that the nonlinear partial differential equations determining the BPS solutions can be derived from a variational principle. The corresponding action enjoys a solution-generating PSL(2, ) symmetry. In certain subcases the system reduces to different known theories, like two-dimensional dilaton gravity or the dimensionally reduced gravitational Chern-Simons theory. We find new supersymmetric solutions including, among others, kinks that interpolate between two AdS4 vacua, electrovac waves on anti-Nariai spacetimes, or generalized Robinson-Trautman solutions. In the case where the Killing vector is null, we obtain a complete classification. The one quarter and one half supersymmetric solutions are determined explicitely, and it is shown that the fraction of three quarters of supersymmetry cannot be preserved. Finally, the general lightlike configuration is uplifted to eleven-dimensional supergravity.

Giant gravitons in AdS/CFT (I): Matrix model and back reaction

In this article we study giant gravitons in the framework of AdS/CFT correspondence. First, we show how to describe these configurations in the CFT side using a matrix model. In this picture, giant gravitons are realized as single excitations high above a Fermi sea, or as deep holes into it. Then, we give a prescription to define quasi-classical states and we recover the known classical solution associated to the CFT dual of a giant graviton that grows in AdS. Second, we use the AdS/CFT dictionary to obtain the supergravity boundary stress tensor of a general state and to holographically reconstruct the bulk metric, obtaining the back reaction of space-time. We find that the space-time response to all the supersymmetric giant graviton states is of the same form, producing the singular BPS limit of the three charge Reissner-Nordstrom-AdS black holes. While computing the boundary stress tensor, we comment on the finite counterterm recently introduced by Liu and Sabra, and connect it to a scheme-dependent conformal anomaly.

Chronology protection in anti-de Sitter

We consider 1/2 BPS excitations of geometries in type IIB string theory that can be mapped into free fermion configurations according to the prescription of Lin, Lunin and Maldacena (LLM). It is shown that whenever the fermionic probability density exceeds one or is negative, closed timelike curves appear in the bulk. A violation of the Pauli exclusion principle in the phase space of the fermions is thus intimately related to causality violation in the dual geometries.

Shaping black holes with free fields

A bstractStarting from a metric Ansatz permitting a weak version of Birkhoff’s theorem we find static black hole solutions including matter in the form of free scalar and p-form fields, with and without a cosmological constant Λ. Single p-form matter fields permit multiple possibilities, including dyonic solutions, self-dual instantons and metrics with Einstein-Kälher horizons. The inclusion of multiple p-forms on the other hand, arranged in a homogeneous fashion with respect to the horizon geometry, permits the construction of higher dimensional dyonic p-form black holes and four dimensional axionic black holes with flat horizons, when Λ < 0. It is found that axionic fields regularize black hole solutions in the sense, for example, of permitting regular — rather than singular — small mass Reissner-Nordstrom type black holes. Their cosmic string and Vaidya versions are also obtained.

AdS/Ricci-flat correspondence and the Gregory-Laflamme instability

We show that for every asymptotically anti–de Sitter (AdS) solution compactified on a torus there is a corresponding Ricci-flat solution obtained by replacing the torus by a sphere, performing a Weyl rescaling of the metric and appropriately analytically continuing the dimension of the torus/sphere (as in generalized dimensional reduction). In particular, it maps Minkowski spacetime to AdS on a torus, the holographic stress energy tensor of AdS to the stress energy tensor due to a brane localized in the interior of spacetime and AdS black branes to (asymptotically flat) Schwarzschild black branes. Applying it to the known solutions describing the hydrodynamic regime in AdS/CFT, we derive the hydrodynamic stress tensor of asymptotically flat black branes to second order, which is constrained by the parent conformal symmetry. We compute the dispersion relation of the Gregory-Laflamme unstable modes through cubic order in the wave number, finding remarkable agreement with numerical data. In the case of no transverse sphere, AdS black branes are mapped to Rindler spacetime and the second-order transport coefficients of the fluid dual to Rindler spacetime are recovered.

Chern-Simons formulation of three-dimensional gravity with torsion and nonmetricity

Abstract We consider various models of three-dimensional gravity with torsion or nonmetricity (metric affine gravity), and show that they can be written as Chern–Simons theories with suitable gauge groups. Using the groups ISO ( 2 , 1 ) , SL ( 2 , C ) and SL ( 2 , R ) × SL ( 2 , R ) , and the fact that they admit two independent coupling constants, we obtain the Mielke–Baekler model for zero, positive and negative effective cosmological constant respectively. Choosing SO ( 3 , 2 ) as the gauge group, one gets a generalization of conformal gravity that has zero torsion and only the trace part of the nonmetricity. This characterizes a Weyl structure. Finally, we present a new topological model of metric affine gravity in three dimensions arising from an SL ( 4 , R ) Chern–Simons theory.

AdS/Ricci-flat correspondence

A bstractWe present a comprehensive analysis of the AdS/Ricci-flat correspondence, a map between a class of asymptotically locally AdS spacetimes and a class of Ricci-flat spacetimes. We provide a detailed derivation of the map, discuss a number of extensions and apply it to a number of important examples, such as AdS on a torus, AdS black branes and fluids/gravity metrics. In particular, the correspondence links the hydrodynamic regime of asymptotically flat black p-branes or the Rindler fluid with that of AdS. It implies that this class of Ricci-flat spacetimes inherits from AdS a generalized conformal symmetry and has a holographic structure. We initiate the discussion of holography by analyzing how the map acts on boundary conditions and holographic 2-point functions.